Reading the Comics, November 7, 2019: The Casual Mentions Edition


As will sometimes happen it’s inconvenient for met to write up a paragraph or two on the particularly mathematically significant comic strips of the past week. Let me here share the comics that just mentioned mathematics, then, and save the heavy stuff for a bit later on.

Bill Watterson’s Calvin and Hobbes repeat for the 5th has Calvin seeking help with an arithmetic problem.

Greg Evans’s Luann Againn for the 6th — a repeat of Luann from the 6th of November, 1991 — sees Gunther thinking out walking to Luann’s house in the language of a word problem. It doesn’t help clear his thoughts.

Jason Chatfield’s Ginger Meggs for the 7th is the sudoku joke for the week.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 7th uses a knowledge of mathematics as shorthand for general knowledge. The strip does misspell “Pythagorean”. This could be a slip on the cartoonists’ part that got past their editors too. Or it could be an extra joke on how often the know-it-all, really, does not. He’ll just talk a confident game long after everyone else has stopped really listening. (I’m a recovering know-it-all myself. I know how our kind thinks.) Or it might be trolling know-it-alls into correcting them.


And this covers things through to Friday’s comics. I write this not having had the chance to read Saturday’s yet. When I do, and when I have the whole week’s strips to discuss, I’ll have it at this link. Furthermore, this week sees the last quarter of the Fall 2019 A to Z under way. I’m excited to learn what I’m doing for the letter ‘U’ also.

Reading the Comics, September 29, 2019: September 29, 2019 Edition


Several of the mathematically-themed comic strips from last week featured the fine art of calculation. So that was set to be my title for this week. Then I realized that all the comics worth some detailed mention were published last Sunday, and I do like essays that are entirely one-day affairs. There are a couple of other comic strips that mentioned mathematics tangentially and I’ll list those later this week.

John Hambrock’s The Brilliant Mind of Edison lee for the 29th has Edison show off an organic computer. This is a person, naturally enough. Everyone can do some arithmetic in their heads, especially if we allow that sometimes approximate answers are often fine. People with good speed and precision have always been wonders, though. The setup may also riff on the ancient joke of mathematicians being ways to turn coffee into theorems. (I would imagine that Hambrock has heard that joke. But it is enough to suppose that he’s aware many adult humans drink coffee.)

Edison: 'Welcome to Edison's Science Sunday. I'm going to show you how to build a simple organic calculator. I'll use a bale of hay, a pot of coffee, and Bob the postman. First, I'll have Bob sit on the hay.' Joules, rat: 'OK, now what?' Edison: 'Bob, what is 46 times 19?' Bob :'874.' Joules: 'You have GOT to be kidding me!' Edison: 'He's a whiz with numbers.' Joules: 'Where does the coffee come in?' Edison: 'It extends Bob's battery life.' Bob: 'Cream and sugar, please.'
John Hambrock’s The Brilliant Mind of Edison lee for the 29th of September, 2019. Essays featuring something mentioned in Edison Lee appear at this link.

John Kovaleski’s Daddy Daze for the 29th sees Paul, the dad, working out the calculations his son (Angus) proposed. It’s a good bit of arithmetic that Paul’s doing in his head. The process of multiplying an insubstantial thing by many, many times until you get something of moderate size happens all the time. Much of integral calculus is based on the idea that we can add together infinitely many infinitesimal numbers, and from that get something understandable on the human scale. Saving nine seconds every other day is useless for actual activities, though. You need a certain fungibility in the thing conserved for the bother to be worth it.

Kid: 'Ba ba'. Dad: 'A brilliant math-related idea?' Kid: 'Ba ba ba ba'. Dad: 'We don't need to wash *all* your toes every time you take a bath since they're not *that* dirty?' 'Ba ba ba ba ba' 'OK, if I've got this. There's 8 space between your 10 toes, each space takes 1.25 seconds to wash. If we wash only one space per bath we save 8.75 seconds each time. Three baths a week, this saves 1365 seconds (22.75 minutes) every year. Gee, what'll we do with all that extra time?' 'Ba ba ba'. 'Play 'This Little Piggy' 107.4 times.'
John Kovaleski’s Daddy Daze for the 29th of September, 2019. This is a new tag. Well, the comic is barely a year old. But this and other essays featuring Daddy Daze should be at this link.

Dan Thompson’s Harley for the 29th gets us into some comic strips not drawn by people named John. The comic has some mathematics in it qualitatively. The observation that you could jump a motorcycle farther, or higher, with more energy, and that you can get energy from rolling downhill. It’s here mostly because of the good fortune that another comic strip did a joke on the same topic, and did it quantitatively. That comic?

Harley, racing on the motorcycle: 'Speeding down this mountain should launch us over Pointy Rock Canyon.' Cat, riding behind: 'How do you figure that?' Harley: 'Math, my friend. Harley + Speed + Ramp = Jump The Canyon. It's so simple, it's genius!' Cat: 'We're going faster than we've ever gone!' Harley: 'I think I heard a sonic boom!' Cat: 'I see the rap!' Harley: 'I see my brilliance!' (They race up the ramp. Final panel, they're floating in space.) Cat: 'Didn't you flunk math in school?' Harley: 'Not the third time.'
Dan Thompson’s Harley for the 29th of September, 2019. This just barely misses being a new tag. This essay and the other time I mentioned Harley are at this link. I’ll keep you up dated if there are more essays to add to this pile.

Bill Amend’s FoxTrot for the 29th. Young prodigies Jason and Marcus are putting serious calculation into their Hot Wheels track and working out the biggest loop-the-loop possible from a starting point. Their calculations are right, of course. Bill Amend, who’d been a physics major, likes putting authentic mathematics and mathematical physics in. The key is making sure the car moves fast enough in the loop that it stays on the track. This means the car experiencing a centrifugal force that’s larger than that of gravity. The centrifugal force on something moving in a circle is proportional to the square of the thing’s speed, and inversely proportional to the radius of the circle. This for a circle in any direction, by the way.

So they need to know, if the car starts at the height A, how fast will it go at the top of the loop, at height B? If the car’s going fast enough at height B to stay on the track, it’s certainly going fast enough to stay on for the rest of the loop.

Diagram on ruled paper showing a track dropping down and circling around, with the conservation-of-energy implications resulting on the conclusion the largest possible loop-the-loop is 4/5 the starting height. Peter: 'I don't think this will work. Your calculations assume no friction.' Jason: 'Peter, please. We're not stupid.' (Jason's friend Marcus is working on the track.) Mom: 'Kids, why is there a Hot Wheels car soaking in a bowl of olive oil?'
Bill Amend’s FoxTrot for the 29th of September, 2019. Essays featuring either the current-run Sunday FoxTrot or the vintage FoxTrot comics from the 90s should be at this link.

The hard part would be figuring the speed at height B. Or it would be hard if we tried calculating the forces, and thus acceleration, of the car along the track. This would be a tedious problem. It would depend on the exact path of the track, for example. And it would be a long integration problem, which is trouble. There aren’t many integrals we can actually calculate directly. Most of the interesting ones we have to do numerically or work on approximations of the actual thing. This is all right, though. We don’t have to do that integral. We can look at potential energy instead. This turns what would be a tedious problem into the first three lines of work. And one of those was “Kinetic Energy = Δ Potential Energy”.

But as Peter observes, this does depend on supposing the track is frictionless. We always do this in basic physics problems. Friction is hard. It does depend on the exact path one follows, for example. And it depends on speed in complicated ways. We can make approximations to allow for friction losses, often based in experiment. Or try to make the problem one that has less friction, as Jason and Marcus are trying to do.

Caption: 'ODDITIONS'. Several people with large numerals as head stand around, reading scripts; the one with a 3 head recites, 'To be or not to be? That is the question.' A 9 leans in, saying, 'Next!'
Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 29th of September, 2019. The occasional essay featuring Mustard and Boloney appears at this link. I feel a bit glad to see this doesn’t seem to be a rerun, or at least it’s not one I’ve discussed before.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 29th is the anthropomorphic numerals joke for the week. This is a slight joke to include here. But there were many comic strips of slight mathematical content. I intend to list them in an essay on Wednesday.

Tuesday I plan to be a day for the Fall 2019 A-to-Z. Again, thank you for reading.

Reading the Comics, October 30, 2018: I Spot An Error Edition


The edition title says it all. Comic Strip Master Command sent me enough strips the past week for two editions and I made an unhappy discovery about one of the comics in today’s.

Dave Coverly’s Speed Bump for the 28th is your anthropomorphic-numerals joke for the week. We get to know the lowest common denominator from fractions. It’s easier to compute anything with a fraction in it if you can put everything under a common denominator. But it’s also — usually — easier to work with smaller denominators than larger ones. It’s always okay to multiply a number by 1. It may not help, but it can always be done. This has the result of multiplying both the numerator and denominator by the same number. So suppose you have something that’s written in terms of sixths, and something else written in terms of eighths. You can multiply the first thing by four-fourths, and the second thing by three-thirds. Then both fractions are in terms of 24ths and your calculation is, probably, easier.

9, talking to 2 at the bar: 'Ah, cheer up, you're not *always* the lowest common denominator.'
Dave Coverly’s Speed Bump for the 28th of October, 2018. So how many different people do you suppose are in an anthropomorphic-numerals world like this?

So this strip is the rare one where I have to say the joke doesn’t work on mathematical grounds. Coverly was mislead by the association between “lowest” and “smallest”. 2 is going to be the lowest common denominator very rarely. Everything in the problem needs to be in terms of even denominators to start with, and even that won’t guarantee it. I hate to do that, since the point of a comic strip is humor and getting any mathematics right is a bonus. But in this case, knowing the terminology shatters the joke. Coverly would have a mathematically valid joke were 9 offering the consolation “you’re not always the greatest common divisor”, the largest number that goes into a set of numbers. But nobody thinks being called the “greatest” anything ever needs consolation, so the joke would fail all but mathematics class.

Teacher: 'Why is it important for today's kids to learn algebra? Because *I* had to learn this junk in school and now it's *your* turn, that's why!'
Randy Glasbergen’s Glasbergen Cartoons for the 29th of October, 2018. It’s a rerun, as you’d tell from the copyright date and awareness that Glasbergen died in 2015. I can’t pin down from when any more than the copyright date gives you, though.

Randy Glasbergen’s Glasbergen Cartoons for the 29th is a joke of the why-learn-mathematics model. “Because we always have done this” is not a reason compelling by the rules of deductive logic. It can have great practical value. Experience can encode things which are hard to state explicitly, or to untangle from one another. And an experienced system will have workarounds for the most obvious problems, ones that a new system will not have. And any attempt at educational reform, however well-planned or meant, must answer parents’ reasonable question of why their child should be your test case.

I do sometimes see algebra attacked as being too little-useful for the class time given. I could see good cases made for spending the time on other fields of mathematics. (Probability and statistics always stands out as potentially useful; the subjects were born from things people urgently needed to know.) I’m not competent to judge those arguments and so shall not.

Baseball player missing his left arm and with a wedge cut out of his shoulder: 'I can't play today, skipper. I gave 110% yesterday.'
Carl Skanberg’s That New Carl Smell for the 29th of October, 2018. Yeah, also, all right, but suppose he only gave 100% yesterday. Wouldn’t that be all of him gone now? I’m saying there are severe logical problems with these implications is all.

Carl Skanberg’s That New Carl Smell for the 29th is a riff on jokes about giving more than 100%. Interpreting this giving-more-than-everything as running a deficit is a reasonable one. I’ve given my usual talk about “100% of what?” enough times now; I don’t need to repeat it until I think of something fresh to say.

Kid in the sandbox: 'You're on a train travelling east at 65 mph and you leave at 7:15. Another train leaves five minutes later heading west ... ' Caption: 'Mensa Schoolyard Bullies'.
Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 30th of October, 2018. I don’t know whether they use real materials to watercolor these illustrations or simply (“simply”, he calls it) digitally paint them for that effect, but it makes for a good appearance and one that I like.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 30th uses mathematics — story problems, specifically — as icons of intelligence. I can’t speak to the Mensa experience, but intellectual types trying to out-do each other? Yes, that’s a thing that happens. I mostly dodge attempts to put me to a fun mathematics puzzle. I’m embarrassed by how long it can take me to actually do one of these, when put on the spot. (I have a similar reaction to people testing my knowledge of trivia in the stuff I actually do know a ridiculous amount about.) Mostly I hope Dave Coverly doesn’t think I’m being this kid.

All of the Reading the Comics posts should be at this link. Essays that include Speed Bump are at this link. I don’t usually have a problem with it. Essays discussing Glasbergen Cartoons should be at this link. They won’t include Glasbergen’s longrunning The Better Half comic, which as far as I can find only ever appeared here the one time anyway. It’s a new tag anyway. Essays with a mention of That New Carl Smell are at this link. It’s a new tag, though, so give it some time if you want to read anything else. Essays with a mention of Mustard and Boloney are at this link. And my Fall 2018 Mathematics A-To-Z should continue for the rest of this calendar year. And it is open for requests for more of the alphabet. Thanks for reading.

Reading the Comics, July 14, 2018: County Fair Edition


The title doesn’t mean anything. My laptop’s random-draw of pictures pulled up one from the county fair last year is all. I’m just working too close to deadline to have a good one. Pet rabbit has surgery scheduled and we are hoping that turns out well for everyone involved.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 12th has the blackboard of mathematical symbols. Familiar old shorthand of conflating mathematics ability with genius, or at least intelligence. The blackboard isn’t particularly full of expressions, possibly because Caulfield and Rouillard’s art might not be able to render too much detail clearly. It’s also got a sort-of appearance of Einstein’s most famous equation. Although with perhaps an extra joke to it. Suppose we’re to take ‘E’ and ‘M’ and ‘C’ to mean what they do in Einstein’s use. Then E - mc^2 has to equal zero. And there are many things you can safely do with zero. Dividing by it, though, isn’t one. I shan’t guess whether Caulfield and Rouillard were being that sly, though.

Blackboard with 'a^2 x 333 / E - MC^2 = 1,333' on it. Nerd: 'Ah! See, I've proved it!' Bully: 'That's nice, now let's step outside and settle this like men.'
Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 12th of July, 2018. Must say that’s some really nice canvas grain and I wonder whether they actually work on media like that for their thrice-a-week comic strip or whether they simply use that texture in their art programs.

Marty Links’s Emmy Lou rerun for the 13th tries to be a paradox. How can one like mathematics without liking figures? But arithmetic is just one part of mathematics. Surely the most-used part, if we go by real-world utility. But not everything. Arithmetic is often useful, yes. But you can do good work in (say) logic or knot theory or geometry with only a slight ability to add or subtract or multiply. There’s not enough emphasis put on that in early education. I suppose it reflects the reasonable feeling that people do need to be competent at arithmetic, which is useful. But it gives one a distorted view of what mathematics can be.

Emmy Lou, looking over her homework, and complaining to her mother: 'Mathematics in itself isn't so hard! It's all these figures ... '
Marty Links’s Emmy Lou rerun for the 13th of July, 2018. Apparently it previously ran the 21st of October, 1971. (I make no claims about even earlier runs of the strip and am just going by what I can make out in the copyright information.)

Mark Parisi’s Off The Markfor the 13th is the anthropomorphic numerals joke for the week. And it presents being multiplied by zero as a terrifying fate for other numbers. This seems to reflect the idea that being multiplied by zero is equivalent to being made into nothing. That it’s being killed. Zero enjoys this dual meaning, culturally, representing both a number and the concept of a thing that doesn’t exist and the concept of non-existence. If being turned from one number to another is a numeral murder, then a 2 sneaking in with a + sign would be at least as horrifying. But that joke wouldn’t work, and I know that too.

Numerals, sweating as a suspenseful scene in a numerals movie: a 9 whistling happily, unsuspecting that a 0 is sneaking into the room and carrying a x sign.
Mark Parisi’s Off The Mark for the 13th of July, 2018. In a moment of comic relief the x slips in the 0’s hand, and it temporarily becomes a + and everybody sighs with relief.

Olivia Jaimes’s Nancy for the 14th is another recreational-mathematics puzzle. I know nothing of Jaimes’s background but apparently it involves a keen interest in that kind of play that either makes someone love or hate mathematics. (Myself, I’m only slightly interested in these kinds of puzzles, most of the time.) This one — add one line to ‘fix’ the equation 5 + 5 + 5 + 5 = 555 — I hadn’t encountered before. Took some fuming to work it out. The obvious answer, of course, is to add a slash across the = sign so that it means “does not equal”.

Teacher: 'Here's today's brainteaser. Can you add just one line to this equation to fix it?' [ 5 + 5 + 5 + 5 = 555 ] Nancy: 'Yep.' (She scribbles a line across the whole equation.)
Olivia Jaimes’s Nancy for the 14th of July, 2018. They … do seem to be spending a lot of time in class for it being July.

But that answer’s dull. What mathematicians like are statements that are true and interesting. There are many things that 5 + 5 + 5 + 5 does not equal. Why single out 555 from that set? So negating the equals sign meets the specifications of the problem, slightly better than Nancy does herself. It doesn’t have the surprise of the answer Nancy’s teacher wants.

If you don’t get how to do it, highlight over the paragraph below for a hint.

There are actually three ways to add the stroke to make this equation true. The three ways are equivalent, though. Notice that the symbols on the board comprise strokes and curves and consider that the meaning of the symbol can be changed by altering the composition of those strokes and curves.

Quincy's Grandmother: 'Who has been your favorite teacher this year, Quincy?' Quincy: 'Well, Mrs Glover sure has made arithmetic relevant. Like this problem. If your pants need a new patch every month ... how many patches would you have in a year and a half?!'
Ted Shearer’s Quincy for the 14th of July, 2018. It originally ran the 21st of May, 1979.

Ted Shearer’s Quincy for the 21st of May, 1979, and rerun the 14th is a joke about making mathematics problems relevant. And, yeah, I’ll give Mrs Glover credit for making problems that reflect stuff students know they’re going to have to deal with. Also that they may have already dealt with and so have some feeling for what plausible answers will be. It’s tough to find many problems like that which don’t repeat themselves too much. (“If your pants need a new patch every two months how many would you have in three years?”).


I do many Reading the Comics posts. Others like this one are here. For other essays that mention Mustard and Boloney, look to this link. I admit I’m surprised there’s anything there; I didn’t remember having written about it before For other discussions of Emmy Lou, try this link. For this and other times I’ve written about Off The Mark try this link. For Nancy content, try this link. And for other Quincy essays you can read this link. Thank you.

Reading the Comics, February 26, 2018: Possible Reruns Edition


Comic Strip Master Command spent most of February making sure I could barely keep up. It didn’t slow down the final week of the month either. Some of the comics were those that I know are in eternal reruns. I don’t think I’m repeating things I’ve already discussed here, but it is so hard to be sure.

Bill Amend’s FoxTrot for the 24th of February has a mathematics problem with a joke answer. The approach to finding the area’s exactly right. It’s easy to find areas of simple shapes like rectangles and triangles and circles and half-circles. Cutting a complicated shape into known shapes, finding those areas, and adding them together works quite well, most of the time. And that’s intuitive enough. There are other approaches. If you can describe the outline of a shape well, you can use an integral along that outline to get the enclosed area. And that amazes me even now. One of the wonders of calculus is that you can swap information about a boundary for information about the interior, and vice-versa. It’s a bit much for even Jason Fox, though.

Jef Mallett’s Frazz for the 25th is a dispute between Mrs Olsen and Caulfield about whether it’s possible to give more than 100 percent. I come down, now as always, on the side that argues it depends what you figure 100 percent is of. If you mean “100% of the effort it’s humanly possible to expend” then yes, there’s no making more than 100% of an effort. But there is an amount of effort reasonable to expect for, say, an in-class quiz. It’s far below the effort one could possibly humanly give. And one could certainly give 105% of that effort, if desired. This happens in the real world, of course. Famously, in the right circles, the Space Shuttle Main Engines normally reached 104% of full throttle during liftoff. That’s because the original specifications for what full throttle would be turned out to be lower than was ultimately needed. And it was easier to plan around running the engines at greater-than-100%-throttle than it was to change all the earlier design documents.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 25th straddles the line between Pi Day jokes and architecture jokes. I think this is a rerun, but am not sure.

Matt Janz’s Out of the Gene Pool rerun for the 25th tosses off a mention of “New Math”. It’s referenced as a subject that’s both very powerful but also impossible for Pop, as an adult, to understand. It’s an interesting denotation. Usually “New Math”, if it’s mentioned at all, is held up as a pointlessly complicated way of doing simple problems. This is, yes, the niche that “Common Core” has taken. But Janz’s strip might be old enough to predate people blaming everything on Common Core. And it might be character, that the father is old enough to have heard of New Math but not anything in the nearly half-century since. It’s an unusual mention in that “New” Math is credited as being good for things. (I’m aware this strip’s a rerun. I had thought I’d mentioned it in an earlier Reading the Comics post, but can’t find it. I am surprised.)

Mark Anderson’s Andertoons for the 26th is a reassuring island of normal calm in these trying times. It’s a student-at-the-blackboard problem.

Morrie Turner’s Wee Pals rerun for the 26th just mentions arithmetic as the sort of homework someone would need help with. This is another one of those reruns I’d have thought has come up here before, but hasn’t.

Reading the Comics, January 20, 2018: Increased Workload Edition


It wasn’t much of an increased workload, really. I mean, none of the comics required that much explanation. But Comic Strip Master Command donated enough topics to me last week that I have a second essay for the week. And here it is; sorry there’s no pictures.

Mark Anderson’s Andertoons for the 17th is the Mark Anderson’s Andertoons we’ve been waiting for. It returns to fractions and their frustrations for its comic point.

Jef Mallet’s Frazz for the 17th talks about story problems, although not to the extent of actually giving one as an example. It’s more about motivating word-problem work.

Mike Thompson’s Grand Avenue for the 17th is an algebra joke. I’d call it a cousin to the joke about mathematics’s ‘x’ not coming back and we can’t say ‘y’. On the 18th was one mentioning mathematics, although in a joke structure that could have been any subject.

Lorrie Ransom’s The Daily Drawing for the 18th is another name-drop of mathematics. I guess it’s easier to use mathematics as the frame for saying something’s just a “problem”. I don’t think of, say, identifying the themes of a story as a problem in the way that finding the roots of a quadratic is.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 18th is an anthropomorphic-geometric-figures joke that I’m all but sure is a rerun I’ve shared here before. I’ll try to remember to check before posting this.

Mikael Wulff and Anders Morgenthaler’s WuMo for the 20th gives us a return of the pie chart joke that seems like it’s been absent a while. Worth including? Eh, why not.

Reading the Comics, April 6, 2017: Abbreviated Week Edition


I’m writing this a little bit early because I’m not able to include the Saturday strips in the roundup. There won’t be enough to make a split week edition; I’ll just add the Saturday strips to next week’s report. In the meanwhile:

Mac King and Bill King’s Magic in a Minute for the 2nd is a magic trick, as the name suggests. It figures out a card by way of shuffling a (partial) deck and getting three (honest) answers from the other participant. If I’m not counting wrongly, you could do this trick with up to 27 cards and still get the right card after three answers. I feel like there should be a way to explain this that’s grounded in information theory, but I’m not able to put that together. I leave the suggestion here for people who see the obvious before I get to it.

Bil Keane and Jeff Keane’s Family Circus (probable) rerun for the 6th reassured me that this was not going to be a single-strip week. And a dubiously included single strip at that. I’m not sure that lotteries are the best use of the knowledge of numbers, but they’re a practical use anyway.

Dolly holds up pads of paper with numbers on them. 'C'mon, PJ, you hafta learn your numbers or else you'll never win the lottery.'
Bil Keane and Jeff Keane’s Family Circus for the 6th of April, 2017. I’m not familiar enough with the evolution of the Family Circus style to say whether this is a rerun, a newly-drawn strip, or an old strip with a new caption. I suppose there is a certain timelessness to it, at least once we get into the era when states sported lotteries again.

Bill Bettwy’s Take It From The Tinkersons for the 6th is part of the universe of students resisting class. I can understand the motivation problem in caring about numbers of apples that satisfy some condition. In the role of distinct objects whose number can be counted or deduced cards are as good as apples. In the role of things to gamble on, cards open up a lot of probability questions. Counting cards is even about how the probability of future events changes as information about the system changes. There’s a lot worth learning there. I wouldn’t try teaching it to elementary school students.

The teacher: 'How many apples will be left, Tillman?' 'When are we going to start counting things more exciting than fruit?' 'What would you like to count, Tillman?' 'Cards.'
Bill Bettwy’s Take It From The Tinkersons for the 6th of April, 2017. That tree in the third panel is a transplant from a Slylock Fox six-differences panel. They’ve been trying to rebuild the population of trees that are sometimes three triangles and sometimes four triangles tall.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 6th uses mathematics as the stuff know-it-alls know. At least I suppose it is; Doctor Know It All speaks of “the pathagorean principle”. I’m assuming that’s meant to be the Pythagorean theorem, although the talk about “in any right triangle the area … ” skews things. You can get to stuf about areas of triangles from the Pythagorean theorem. One of the shorter proofs of it depends on the areas of the squares of the three sides of a right triangle. But it’s not what people typically think of right away. But he wouldn’t be the first know-it-all to start blathering on the assumption that people aren’t really listening. It’s common enough to suppose someone who speaks confidently and at length must know something.

Dave Whamond’s Reality Check for the 6th is a welcome return to anthropomorphic-numerals humor. Been a while.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 6th builds on the form of a classic puzzle, about a sequence indexed to the squares of a chessboard. The story being riffed on is a bit of mathematical legend. The King offered the inventor of chess any reward. The inventor asked for one grain of wheat for the first square, two grains for the second square, four grains for the third square, eight grains for the fourth square, and so on, through all 64 squares. An extravagant reward, but surely one within the king’s power to grant, right? And of course not: by the 64th doubling the amount of wheat involved is so enormous it’s impossibly great wealth.

The father’s offer is meant to evoke that. But he phrases it in a deceptive way, “one penny for the first square, two for the second, and so on”. That “and so on” is the key. Listing a sequence and ending “and so on” is incomplete. The sequence can go in absolutely any direction after the given examples and not be inconsistent. There is no way to pick a single extrapolation as the only logical choice.

We do it anyway, though. Even mathematicians say “and so on”. This is because we usually stick to a couple popular extrapolations. We suppose things follow a couple common patterns. They’re polynomials. Or they’re exponentials. Or they’re sine waves. If they’re polynomials, they’re lower-order polynomials. Things like that. Most of the time we’re not trying to trick our fellow mathematicians. Or we know we’re modeling things with some physical base and we have reason to expect some particular type of function.

In this case, the $1.27 total is consistent with getting two cents for every chess square after the first. There are infinitely many other patterns that would work, and the kid would have been wise to ask for what precisely “and so on” meant before choosing.

Berkeley Breathed’s Bloom County 2017 for the 7th is the climax of a little story in which Oliver Wendell Holmes has been annoying people by shoving scientific explanations of things into their otherwise pleasant days. It’s a habit some scientifically-minded folks have, and it’s an annoying one. Many of us outgrow it. Anyway, this strip is about the curious evidence suggesting that the universe is not just expanding, but accelerating its expansion. There are mathematical models which allow this to happen. When developing General Relativity, Albert Einstein included a Cosmological Constant for little reason besides that without it, his model would suggest the universe was of a finite age and had expanded from an infinitesimally small origin. He had grown up without anyone knowing of any evidence that the size of the universe was a thing that could change.

Anyway, the Cosmological Constant is a puzzle. We can find values that seem to match what we observe, but we don’t know of a good reason it should be there. We sciencey types like to have models that match data, but we appreciate more knowing why the models look like that and not anything else. So it’s a good problem some of the cosmologists have been working on. But we’ve been here before. A great deal of physics, especially in the 20th Century, has been driven by looking for reasons behind what look like arbitrary points in a successful model. If Oliver were better-versed in the history of science — something scientifically minded people are often weak on, myself included — he’d be less easily taunted by Opus.

Mikael Wulff and Anders Morgenthaler’s TruthFacts for the 7th thinks that we forgot they ran this same strip back on the 17th of March. I spotted it, though. Nyah.